Related papers: Complex balanced equilibria of weakly reversible p…
This paper studies stability analysis of DC microgrids with uncertain constant power loads (CPLs). It is well known that CPLs have negative impedance effects, which may cause instability in a DC microgrid. Existing works often study the…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
Port-Hamiltonian (pH) systems offer a highly structured and energy-based modular framework for control systems. Many pH systems exhibit non-polynomial non-linearities. We consider the problem of immersing such systems into a…
Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions with two chemical species and arbitrary power-law kinetics. We study existence,…
Self-assembling, semi-flexible polymers are ubiquitous in biology and technology. However, there remain conflicting accounts of the equilibrium kinetics for such an important system. Here, by focusing on a dynamical description of a minimal…
Linear Parameter-Varying (LPV) systems with piecewise differentiable parameters is a class of LPV systems for which no proper analysis conditions have been obtained so far. To fill this gap, we propose an approach based on the theory of…
For a reaction network with species set $\mathscr{S}$, a log-parametrized (LP) set is a non-empty set of the form $E(P, x^*) = \{x \in \mathbb{R}^\mathscr{S}_> \mid \log x - \log x^* \in P^\perp\}$ where $P$ (called the LP set's flux…
The kinetic description of relativistic plasmas in the presence of time-varying and spatially non-uniform electromagnetic fields is a fundamental theoretical issue both in astrophysics and plasma physics. This refers, in particular, to the…
Power law systems have been studied extensively due to their wide-ranging applications, particularly in chemistry. In this work, we focus on power law systems that can be decomposed into stoichiometrically independent subsystems. We show…
This paper discusses some links properties of operators with the well- known physical concepts of hyperstability, passivity, energy dissipativeness and conservativeness with positive realness properties of the transfer functions in linear…
We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
Many-body systems relaxing to equilibrium can exhibit complex dynamics even if their steady state is trivial. At low temperatures or high densities their evolution is often dominated by steric hindrances affecting particle motion [1,2,3].…
Neural-based, data-driven analysis and control of dynamical systems have been recently investigated and have shown great promise, e.g. for safety verification or stability analysis. Indeed, not only do neural networks allow for an entirely…
This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws. The basic idea is that the "meaningful objects" are the fluxes, evaluated across domain…
Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…
A complex balanced kinetic system is absolutely complex balanced (ACB) if every positive equilibrium is complex balanced. Two results on absolute complex balancing were foundational for modern chemical reaction network theory (CRNT): in…
Generalized mass-action systems are power-law dynamical systems arising from chemical reaction networks. Essentially, every nonnegative ODE model used in chemistry and biology (for example, in ecology and epidemiology) and even in economics…
Power law is one of the the simplest forms of the relationship between different variables of a system. It leads naturally to the introduction of compound parameters describing physical properties of the system. Often one of the variables…
We consider the dynamics of continuously measured many-body chaotic quantum systems. Focusing on the observable of state purification, we analytically describe the limits of strong and weak measurement rate, where in the latter case…